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I would say a good start is to just use the airplane mode of your phone. That should disable your RF transmitter. But of course you wont be notified when the network is paging your IMSI.
The save option is to use a phone with OsmocomBB, a free software implementation of the GSM stack:
http://bb.osmocom.org/trac/
It has limited functionality (no GPRS working at the moment) but at least you know exactly would your phone is doing. With that, you can even run CatcherCatcher, which is able to detect IMSI catchers:
http://opensource.srlabs.de/projects/catcher
The supported phones are a bit outdated, mostly old Motorola phones. But there is one supported smartphone: the Openmoko Freerunner. It is pretty usable these days and is fully supported by Debian. I love it, but you will need to tinker - a lot.

That is a bold claim. Whether you are dead or not would definitely depend on your definition of death. In my opinion consciousness is locked to a point in time (and to the configuration of the brain). So, in order to be in line with your notion of death, "you" die every moment.

You do not touch my point. You seem to agree that a conscious entity arises due to information evolving over time. Let us keep this assumption.

For the sake of the argument let us further assume that everything you described is actually possible and that you can transform into a conscious entity experiencing infinite subjective time. Even then entropy flies in the face of your argument. The problem is that you cannot conserve information indefinitely - even if you try with all the resources in the world. Sure, you would have a conscious being experiencing time continuously. But after waiting sufficiently long that entity would have absolutely no information about the present day. It wouldn't share any information with you. This does not only include memories but also behavioral patterns, world views and so forth. That being could have evolved from any other being living today, you wouldn't be able to tell. Thus, that being won't be you given any sane definition of identity. You would be gone for sure.

Several of your other assumptions are very strong. Everything you describe is discrete: computation steps, finite state machines. The brain is not discrete and simulating it exactly using a finite state machine is impossible. You might argue that you can simulate it with arbitrary precision given enough resources and that might be sufficient depending on your notion of identity. It is my personal belief that this is impractical. (As a side note I am convinced that the notion of an evolving consciousness per se is all rubbish anyway; if you could generate an exact copy of yourself, which one would be 'you', the copy or the original? None, obviously. Consciousness is fixed to a point in time.)

In any case information degradation is a fundamental problem for immortality.

I'm not worried about the human body. I'm worried about the information that represents 'you'. You would have a dynamical system (your consciousness) evolving over the millennia which at the end would have nothing in common with the 'you' of today. I agree that there is an implicit materialistic assumption about the self, though.